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Proof step 164 from proof inv-addn (previous step)

# lax0 = # gndx0, # lax = # gndx, gstore3 ↓[nx0.last].gndlist = gndx0, gstore3 ↓[nx0.last].ladrlist = lax0, gstore3[nx0.last] = groupblock(gndx0, lax0, m0), abs-log(nx0, gstore3 ↓) = abs-log(nx1, gstore2 ↓), nodes(gstore3 ↓, jro0) = nodes(gstore2 ↓, jro1), remove-refsize0(gstore0) = gstore0, elems nx1 ∩ jro1 = ∅, (nx0.toSet \ nx1.toSet) ∩ dom gstore2 = ∅, elems nx0 ∩ jro0 = ∅, dom gstore0 ∪ elems nx1 = dom gstore2 ∪ jro1, dom gstore0 ∪ elems nx0 = dom gstore3 ∪ jro0, p_os < pmaxino, fi2.inos < jmaxino1, fi1.inos < pmaxino, inv(groupblock(gndx0, lax0, m0)), inv(groupblock(gndx0 + gndx, lax0 + lax, m0)), inv(gstore0), inv(gstore2 \ jro1), inv(gstore3 \ jro0), inv-flashsize(gndx, lax), refsize-cons(gstore3[nx0.last, groupblock(gndx0 + gndx, lax0 + lax, m0)], range fi2), refsize-cons(gstore2, range fi2), refsize-cons(gstore0, range fi1), refsize-cons(gstore3, range fi2), ri-inj(fi2), ri-inj(fi1), transaction(ndx, gndx), valid-journal-head(nx0, gstore3, jro0), nx0.last ∈ gstore3, nx0.last ∈ gstore3 ↓, pmaxino ≤ jmaxino1, fi2.lebs ⊆ dom gstore3, fi2.lebs ⊆ dom gstore2, fi1.lebs ⊆ dom gstore0, dom gstore2 ⊆ dom gstore3, jvalid4 ∧ nx1 ≠ [] → valid-journal-head(nx1, gstore2, jro1) ⊦ gndx = [], nx0 = [], pmaxino = 0, dups(nx1), dups(nx0), dups(lax), dups(lax0 + lax), nx0.last ∈ jro0, new(lax.to-adr(nx0.last), nodes(gstore2 ↓, jro1)) ∧ nodes(gstore3 ↓, jro0)[lax.to-adr(nx0.last), ndx] = nodes(gstore2 ↓, jro1)[lax.to-adr(nx0.last), ndx] ∧ abs-log(nx0.butlast, gstore3 ↓) + lax0.to-adr(nx0.last) = abs-log(nx1, gstore2 ↓) ∧ valid-journal-head(nx0, gstore3[nx0.last, groupblock(gndx0 + gndx, lax0 + lax, m0)], jro0)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 165:
# gstore3[nx0.last] ↓.ladrlist = # gstore3[nx0.last] ↓.gndlist, # lax = # gndx, gstore3[nx0.last] = groupblock(gstore3[nx0.last] ↓.gndlist, gstore3[nx0.last] ↓.ladrlist, m0), abs-log(nx0, gstore3 ↓) = abs-log(nx1, gstore2 ↓), nodes(gstore3 ↓, jro0) = nodes(gstore2 ↓, jro1), remove-refsize0(gstore0) = gstore0, elems nx1 ∩ jro1 = ∅, (nx0.toSet \ nx1.toSet) ∩ dom gstore2 = ∅, elems nx0 ∩ jro0 = ∅, dom gstore0 ∪ elems nx1 = dom gstore2 ∪ jro1, dom gstore0 ∪ elems nx0 = dom gstore3 ∪ jro0, p_os < pmaxino, fi2.inos < jmaxino1, fi1.inos < pmaxino, inv(gstore3[nx0.last]), inv(groupblock(gstore3[nx0.last] ↓.gndlist + gndx, gstore3[nx0.last] ↓.ladrlist + lax, m0)), inv(gstore0), inv(gstore2 \ jro1), inv(gstore3 \ jro0), inv-flashsize(gndx, lax), refsize-cons(gstore3[nx0.last, groupblock(gstore3[nx0.last] ↓.gndlist + gndx, gstore3[nx0.last] ↓.ladrlist + lax, m0)], range fi2), refsize-cons(gstore2, range fi2), refsize-cons(gstore0, range fi1), refsize-cons(gstore3, range fi2), ri-inj(fi2), ri-inj(fi1), transaction(ndx, gndx), valid-journal-head(nx0, gstore3, jro0), nx0.last ∈ gstore3, pmaxino ≤ jmaxino1, fi2.lebs ⊆ dom gstore3, fi2.lebs ⊆ dom gstore2, fi1.lebs ⊆ dom gstore0, dom gstore2 ⊆ dom gstore3, jvalid4 ∧ nx1 ≠ [] → valid-journal-head(nx1, gstore2, jro1) ⊦ gndx = [], nx0 = [], pmaxino = 0, dups(nx1), dups(nx0), dups(lax), new(lax.to-adr(nx0.last), nodes(gstore2 ↓, jro1)) ∧ abs-log(nx0.butlast, gstore3 ↓) + gstore3[nx0.last] ↓.ladrlist.to-adr(nx0.last) = abs-log(nx1, gstore2 ↓) ∧ valid-journal-head(nx0, gstore3[nx0.last, groupblock(gstore3[nx0.last] ↓.gndlist + gndx, gstore3[nx0.last] ↓.ladrlist + lax, m0)], jro0)

Rule argument

Additional information

Used simplifier rules: lf-inv-append-sizes: ⊦ # gndx1 = # lax1 ∧ inv(groupblock(gndx0 + gndx1, lax0 + lax1, m)) → # gndx0 = # lax0;%a: ⊦ (lax + lax0) + lax1 = lax + lax0 + lax1; from specification list[laddress-list]%a: ⊦ (gndx + gndx0) + gndx1 = gndx + gndx0 + gndx1; from specification list[group-store]% ⊦ inv(groupblock(gndx, lax, m0)) → ¬ dups(lax); (s)% ⊦ elems nx ∩ ginval = ∅ ∧ nx ≠ [] → ¬ nx.last ∈ ginval; (s)%int-c: ⊦ ns ∩ ns0 = ns0 ∩ ns; from specification set-union[nat-set]%int-a: ⊦ (ns ∩ ns0) ∩ ns1 = ns ∩ ns0 ∩ ns1; from specification set-union[nat-set]% ⊦ n ∈ gstore ↓ ↔ n ∈ gstore; (s)% ⊦ n ∈ gstore → gstore ↓[n] = gstore[n] ↓; (s)